"Silver age Chronology: When did the Kents die?"
"Young Clark, as Superboy, took them on an 'adventure vacation' to a spot nobody'd been to for a long time. Seemed a virus existed there that hadn't been seen in just as long a time.
"The Kents caught it. Conveniently, only adults were affected, and teens were immune. Back home, Clark could get away with nursing them without anyone suspecting anything. Lana helped.
"They died not long after returning to Smallville."
WELL, YOU'RE ALL around it, Niddle.
The story of the Kents' death was told in "The Last Days of Ma and Pa Kent", from Superman # 161 (May, 1963).
As the tale describes, Jonathan and Martha Kent are enjoying a vacation on a Caribbean island, having travelled there via a pleasure cruiser built for them by their son, Superboy. While digging for specimens to add to Jonathan's sea-shell collexion, the couple unearth a buried pirate chest containing a pair of flintlock pistols, a cutlass, and a piece of parchment. The fragment of parchment is from the diary of Pegleg Morgan, and it contains the information that on 16 July 1717, he was marooned on the very island upon which the Kents are vacationing.
When the Boy of Steel drops by to see how his foster-parents are enjoying their holiday, they ask him to take them to the past to check on what happened to Pegleg Morgan. The ever-dutiful son, Superboy surrounds the cruiser with a friction-proof bubble and transports the three of them to the date that Morgan was marooned on the island. There they discover that the infamous Blackbeard was responsible for exiling Morgan to the island. As Blackbeard puts it, "You heard me, Pegleg Morgan! You're a menace . . . a danger to my ship! We're abandoning you here on this island!"
There is a brief interlude in which Blackbeard and the rest of his crew discover Superboy's presence on the island. While his parents watch from hiding, the Boy of Steel uses his super-powers to, essentially, spook the hell out the pirates. Then he returns himself and the Kents to their own time and home to Smallville.
The next morning, the Kents awaken with raging fevers. Clark calls the family doctor who, alarmedly, calls in other physicians for consultation. Their diagnosis is that the Kents have contracted the Caribbean fever plague. What mystifies the doctors, though, is that the Caribbean fever plague has been extinct for the last one hundred years. (And, obviously, Clark cannot tell them that he had taken them on a time-trip to 1717 without revealing his Superboy identity.)
It gets worse. The Caribbean fever plague is inevitably fatal. There is no cure.
As you said, the disease affects only adults, so it doesn't raise suspicion that Clark--who is immune to the disease, anyway--is able to care for his parents. And Lana Lang pitches in.
Examining historical records, Clark learns of a possible cure--the sap of a giant orchid tree of the Brazilian jungle. As Superboy, he procures this, but it fails to cure the Kents, who have lapsed into comas.
Young Lex Luthor offers to use one of his inventions, the vibro-health restorer, on the Kents, in the hope that if Jonathan Kent, who serves on the prison parole board, survives, he will put in a good word for Luthor. Unfortunately, Luthor's device fails to restore the stricken couple to health.
Then Superboy gets the idea of casting his parents into the Phantom Zone where their lives will be preserved until he can find a cure. Retrieving the Phantom-Zone projector, he turns it on his parents. However, at this particular time, sunspot activity on our sun has created a magnetic storm on Earth, and the magnetic storm interferes with the operation of the Phantom-Zone projector. The projector has stopped working.
Martha Kent dies. Jonathan Kent regains consciousness long enough to have a final word with his son, then he passes away, as well.
As Clark goes through the details of closing out his parents' lives, he blames himself for their deaths. He feels that had he not taken them back to 1717, then they would not have contracted the Caribbean fever plague. Deciding that it was his super-powers that caused their deaths, he abandons his Superboy identity and forswears using his powers ever, again.
Clark decides to sell the Kent home (a decision he later reverses; also note, as Jon Clark pointed out, this is not the Kent farm--Pa Kent sold the farm, bought the general store, and moved his family inside Smallville's limits just before Clark was old enough to attend school). While taking inventory of his father's property, he discovers the items Ma and Pa found in the old pirate chest. Spotting the fragment from Pegleg Morgan's diary, he recalls seeing the missing piece in the museum where he had sought to find a cure for his parents.
Returning to the museum, Clark matches the two pieces of the page and discovers that Pegleg Morgan had had the Caribbean fever plague and Blackbeard marooned him on that island before he could infect the rest of the pirate captain's crew. He then asks the curator to check the museum records; Clark learns that the sea captain who donated Morgan's diary to the museum and the man who installed it the display case both died of a mysterious fever. Clark deduces that it is the diary itself which is infected with the Caribbean fever plague virus.
Therefore, Ma and Pa Kent did not contract the Caribbean fever plague because Superboy took them to the past. They were infected by the disease when they opened Morgan's chest and found the parchment--a torn page from Morgan's diary. They had inadvertently doomed themselves before Superboy arrived on the island and took them to the past.
Knowing now that his super-powers were not responsible for his parents' deaths, Clark decontaminates Morgan's diary with a burst of heat vision and resumes his career as Superboy.
Also, as Jon Clark accurately pointed out, according to the pre-Crisis Superman's personal history, the Kents died in the summer following Clark's graduation from high school and before he started college.
Hope this helps.